When three scholars, all trained in generally the same mainstream critical methods, debate an issue such as this, perhaps it isn't much of a surprise that the disagreements aren't great.
Alan emphasizes the problems in deriving any historically reliable data from the infancy accounts in Matthew and Luke, problems that Larry readily acknowledges—even though he would like to argue that the tradition of the virginal conception is earlier than the Matthew and Luke accounts, which were composed in the last quarter of the first century (or, in Luke's case, I think perhaps even later). Alan also stresses the force of the criterion of dissimilarity, in reducing quite severely what critical scholars can say with any confidence about the historical Jesus. His list—that Jesus was baptized by John; that he held views about the coming of the kingdom (I'm rephrasing Alan here, since the "end of the world" really isn't an apocalyptic notion); that he opposed the Temple in some way; and that he was crucified by the Romans—is not only very short and mostly uncontroversial but also doesn't include anything about the details of Jesus' birth.
I'm fully in accord with Alan's conclusion that good historical reasoning should make us cautious about the historical claims that are implicit—or that seem to be implicit—in religious claims. Larry is not in principle in disagreement with this conclusion either, though he would like to make a bit more of the tradition of the virginal conception as at least "early" and of Jewish-Christian rather than pagan provenance. Given the character of both Matthew's and Luke's infancy accounts, with their rich evocation of themes from the Hebrew Bible, this seems a perfectly reasonable conclusion. This we can say as historians of tradition.
But there is an easy confusion between statements of empirical fact and statements of value and belief. We need to be cautious about which is which, especially in the documents that we study, which don't make this distinction at all. As the philosopher Ludwig Wittgenstein puts it, "there is a great difference between disagreements as to whether there is a Last Judgment and whether there is a German airplane overhead." The point is not simply that one cannot verify empirically that there is a Last Judgment; the point is that the statements are of a different order. Statements of empirical fact can be probabilistic; we can hedge our bets. The plane above my head is perhaps German but it could be American; or maybe it isn't a plane at all—maybe it's a bird. It would be odd to say, however, "I believe that there might be a Last Judgment" or "It is probable that God spoke to Moses but I'm really not sure." Religious beliefs are not merely probabilistic, for in that case they would be, as the philosopher David Hume argued a propos of miracles, far less probable than most of the other beliefs we hold about the world—in other words, hardly worth holding at all.
To apply this to the debate at hand: I take the belief in the virginal conception to be a statement of religious belief—that is, a theological statement in Larry's terminology. Therefore, it is wrong to confuse it with a statement about gynecology or embryology. That doesn't make it "less" than an empirical statement any more than "murder is a crime" or "the maintenance of human dignity is a good" are of less value or importance than empirical statements. This also means, however, that whether I can trace the tradition of the virginal conception to a stage earlier than, say, A.D. 80, or A.D. 70, or A.D. 40—all of which would be tentative, historical, and probabilistic conclusions—has nothing to do with the meaning and function of the belief in the virginal conception as a religious belief. So in that sense, I agree fully with Alan that there is no reason why Christians ought to stop celebrating Christmas, or Jews Hanukkah, since the beliefs involved in those two celebrations are not the kind of beliefs that are empirical or need historical foundation.
The story of the oil of the Maccabees and the stories of Jesus' birth are great stories. To adapt a sentence from Norman McLean's A River Runs Through It, they are not true stories, but they are stories that are true.